In communications systems, carrier recovery is used for estimation and compensation of faults, such as carrier phase and frequency offset, which occurs between a received communications signal's carrier wave and the receiver's local oscillator. The concept of carrier recovery is well known in the art and widely used in wireless communication systems.
Algorithms for carrier recovery used in Single-Input Single-Output (SISO) communications systems can generally also be directly applied to Multiple-Input Multiple-Output (MIMO) communications systems as long as all transmitters share the same oscillator and correspondingly all receivers are clocked by a common oscillator. However, in communications systems where all transmitters and receivers are clocked by independent oscillators, existing carrier recovery solutions cannot be utilized. The case is further complicated if time-asynchronous transmission from all antennas is considered, and the channel transfer function is frequency selective.